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BK

Providence : American Mathematical Society, [2015]

xviii, 759 stran : ilustrace ; 27 cm

ISBN 978-1-4704-1102-2 (vázáno)

Obsahuje bibliografii na stranách 691-735 a rejstříky

001458379

Contents // Preface to the Series xi // Preface to Part 3 xvii // Chapter 1. Preliminaries 1 // §1.1. Notation and Terminology 1 // §1.2. Some Results for Real Analysis 3 // §1.3. Some Results from Complex Analysis 12 // §1.4. Green’s Theorem 16 // Chapter 2. Pointwise Convergence Almost Everywhere 19 // §2.1. The Magic of Maximal Functions 22 // §2.2. Distribution Functions, Weak-L1, and Interpolation 26 // §2.3. The Hardy-Littlewood Maximal Inequality 41 // §2.4. Differentiation and Convolution 52 // §2.5. Comparison of Measures 60 // §2.6. The Maximal and Birkhoff Ergodic Theorems 65 // §2.7. Applications of the Ergodic Theorems 92 // §2.8. Bonus Section: More Applications of the Ergodic Theorems 102 // §2.9. Bonus Section: Subadditive Ergodic Theorem and Lyapunov Behavior 133 // §2.10. Martingale Inequalities and Convergence 147 // §2.11. The Christ-Kiselev Maximal Inequality and Pointwise Convergence of Fourier Transforms 168 // Chapter 3. Harmonic and Subharmonic Functions 173 // §3.1. Harmonic Functions 177 // §3.2. Subharmonic Functions 202 // §3.3. Bonus Section: The Eremenko-Sodin Proof of Picard’s // Theorem 213 // §3.4. Perron’s Method, Barriers, and Solution of the Dirichlet // Problem 220 // §3.5. Spherical Harmonics 232 // §3.6. Potential Theory 252 // §3.7. Bonus Section: Polynomials and Potential Theory 278 // §3.8. Harmonic Function Theory of Riemann Surfaces 298 // Chapter 4. Bonus Chapter: Phase Space Analysis 319 // §4.1. The Uncertainty Principle 320 // §4.2. The Wavefront Sets and Products of Distributions 345 // §4.3. Microlocal Analysis: A First Glimpse 352 // §4.4. Coherent States 373 // §4.5. Gabor Lattices 390 // §4.6. Wavelets 407 // Chapter 5. Hp Spaces and Boundary Values of Analytic Functions on the Unit Disk 437 // §5.1. Basic Properties of Hp 439 // §5.2. H2 444 // §5.3. First Factorization (Riesz) and Hp 450 //

§5.4. Carathéodory Functions, h1, and the Herglotz // Representation 459 // §5.5. Boundary Value Measures 464 // §5.6. Second Factorization (Inner and Outer Functions) 468 // §5.7. Conjugate Functions and M. Riesz’s Theorem 472 // §5.8. Homogeneous Spaces and Convergence of Fourier Series 493 // §5.9. Boundary Values of Analytic Functions in the Upper // Half-Plane 498 // §5.10. Beurling’s Theorem 515 // §5.11. Hp-Duality and BMO 517 // §5.12. Collar’s Theorem on Ergodic Hilbert Transforms 539 // Contents ix // Chapter 6. Bonus Chapter: More Inequalities 543 // §6.1. Lorentz Spaces and Real Interpolation 547 // §6.2. Hardy-Littlewood-Sobolev and Stein-Weiss Inequalities 559 // §6.3. Sobolev Spaces; Sobolev and Rellich-Kondrachov // Embedding Theorems 565 // §6.4. The Calderón-Zygmund Method 588 // §6.5. Pseudodifferential Operators on Sobolev Spaces and the // Calderon-Vaillancourt Theorem 604 // §6.6. Hypercontractivity and Logarithmic Sobolev Inequalities 615 // §6.7. Lieb-Thirring and Cwikel-Lieb-Rosenblum Inequalities 657 // §6.8. Restriction to Submanifolds 671 // §6.9. Tauberian Theorems 686 // Bibliography 691 // Symbol Index 737 // Subject Index 739 // Author Index 751 // Index of Capsule Biographies